**Title:** What does it mean to be glassy, and why 3-tensors are so much harder than matrices.

**Speaker:** Pax Kivimae

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

Giorgio Parsi, a pioneer in the physics of glasses, won half of the 2021 Nobel prize in physics for his work. Crucially though, the award barely mentions structural glasses, like the ones composing our windows, and focuses on the applications of his work to "glassy" problems in machine learning, biology, and black hole cosmology. This has the fun effect of injecting a bunch of old glassblowing terms into a number of fields, but if it doesn't refer to the material, then what does glassy mean? The focus of this talk will be to illustrate its meaning through a concrete example of a glassy system: a large random 3-tensor. We will try to illustrate glassy concepts in terms of the explicit properties of this object.For the physically uninterested, the glassy properties of this random object come mostly from the (non-random) breakdown of most classical linear algebra facts when generalized to p-tensors for p>2. In this way, the talk also addresses the problems with higher tensor algebra, and the randomness is used to show that these problems are not just the exception, they are in some sense the norm.

Copyright © 1997-2024 Department of Mathematics, Northwestern University.